摘要
Local fluid flow（LFF） at the mesoscopic scale is the main dissipation mechanism of seismic waves in heterogeneous porous media within the seismic frequency band.LFF is easily influenced by the structure and boundary conditions of the porous media,which leads to different behaviors of the peak frequency of attenuation.The associated transition frequency can provide detailed information about the trend of LFF;therefore,research on the transition frequency of LFF and its relationship with the peak frequency of the corresponding attenuation（i.e.,inverse of quality factor） facilitates the detailed understanding of the effect of inner structures and boundary conditions in porous media.In this study,we firstly obtain the transition frequency of fluid flux based on Biot＇s theory of poroelasticity and the fast Fourier transform algorithm in a sample containing one repeating unit cell（RUC）.We then analyze changes of these two frequencies in porous media with different porous properties.Finally,we extend our analysis to the influence of the undrained boundary condition on the transition frequency and peak frequency in porous media with multiple RUCs.This setup can facilitate the understanding of the effect from the undrained boundary condition.Results demonstrate that these two frequencies have the same trend at low water saturation,but amplitude variations differ between the frequencies as the amount of saturation increases.However,for cases of high water saturation,both the trend and the amplitude variation of these two frequencies fit well with each other.
在地震频段内,中观尺度局域流是引起孔隙岩层速度频散与衰减的主要原因,研究中观尺度孔隙中局域流的过渡频率及其对应的衰减(逆品质因子)峰值频率之间的关系,有助于深入分析孔隙介质内部构造的细节。基于Biot孔隙弹性理论得出时间域内局域流流体通量,引入傅立叶变换得到频域上的流体通量。为避免不同单元体之间局域流的相互影响,建立双相孔隙介质单重单元体模型,并且在流体通量基础上选择含水层的过渡频率来等价局域流的过渡频率。此外,针对不同孔隙介质参数,分析了局域流整体过渡频率及相应的衰减峰值频率的变化特征。为了了解边界条件对计算结果造成的影响,建立了多重单元体模型,引出局部局域流过渡频率及相应的衰减峰值频率。数值模拟结果表明,在低饱和度状态下,两种频率的变化趋势相同,但变化幅度存在较大差异;在高饱和度状态下,两种频率的变化趋势与变化幅度都很接近。
基金
supported by National Natural Science Foundation of China(Grant No.41374116)
the Fundamental Research Funds for Central Universities(Grant No.2014B39014)
